A convex lens of focal length 20 cm is placed coaxially with a convex mirror of radius of curvature 20 cm. The two are kept 15 cm apart. A point object is placed 40 cm in front of the convex lens. Find the position of the image formed by this combination. Draw the ray diagram showing the image formation.

#### Solution

Let us first locate the image of the point object S formed by the convex lens.

Here:*u *= -40 cm

And, *f* = 20 cm

From the lens formula, we have:

`1/v-1/u=1/f`

`=>1/v=1/f+1/u`

`=>1/v=1/20+1/(-40)`

`=>1/v=(2-1)/40=1/40`

⇒ v = 40 cm

The positive sign shows that the image is formed to the right of the lens as shown in the following figure.

The image I_{1} is formed behind the mirror and hence acts as a virtual source for the mirror. The convex mirror forms the image I_{2}, whose distance from the mirror can be calculated as:

`1/v+1/u=1/f`

Here:

u = 25 cm

And `f= R/2=10 cm`

`=>1/v=1/f-1/u`

`=>1/v=1/10-1/25`

`=>1/v=(5-2)/50=3/50`

⇒ v = 16.67 cm

Hence, the final image is formed at a distance of 16.67 cm from the convex mirror as shown in the following figure.'